Hi, kinjiGC,
I am happy to respond…I appreciate your doubt, however, not very sure whether I would be able to help you the best, as my reasoning is drawn out of my observations. An expert would do well do endorse my reasoning…btw here are my thoughts…
To begin with, in your sentence:
I have a better bat than my brother does…CORRECT
I have a better bat than my brother has….(as is your ‘expected’ interpretation)…
WRONG In fact this sentence should be correctly modified to ‘
I have a better bat than the onethat my brother has.’
Two reasons:1. As a general rule, if the main verb is a transitive verb and is itself used to complete the clause following
than in a comparison sentence involving an object-object comparison, it should be followed by its object. However, helping verbs can be used to substitute the main verb and end such a sentence without mentioning
(though not always) the direct object of comparison in the clause following
than.
2. ‘Have’ in this context is a transitive verb.
To illustrate these reasons, let us consider a few examples below.
SET1: (Note all verbs in sentences 1 to 5 are either intransitive or non-transitive)
1. Kate walks faster than Jim walks.
2. Humans live for a shorter span of time than turtles live.
3. Andy is taller than Bill is.
4. Apples are more healthy to eat than caramels are.
(Taken from MGMAT SC guide, pg.130)5. Today, Mr. Clarke has left for home earlier than he had left the day before
.
SET 2: (Note all verbs in sentences 6 to 10 are transitive)
6. Cezanne likes Andy more than she likes Bill.
7. His sister slaps him harder than his brother slaps him.
8. I have dreamt of going to Harvard more than I have dreamt of just starting up a new business venture.
9. I drive the car faster than my brother drives it.
10.
(Finally, let’s take your sentence) I have a better bat than
the one that my brother has.
Now ponder over the 2nd set (sentences 6 to 10) and let us re-write these sentences after omitting the object of the verb, after
than 6. Cezanne likes Andy more than she likes. …(likes whom?)
7. His sister slaps him harder than his brother slaps …(slaps whom?)
8. I have dreamt of going to Harvard more than I have dreamt ….(dreamt of what?)
9. I drive the car faster than my brother drives …(drives what?)
10.
I have a better bat than my brother has …(has what?)...
(the way you wrote it)Do you notice that these sentences (after omitting the object following
than) sound incomplete? However, sentences 1 to 5 are fine the way they are. This substantiates my point no. 1 that if the sentence has a transitive verb,
the object of which is undergoing comparison in some way, and if the same verb is used to complete the clause that follows
than, THE VERB IN THIS CLAUSE SHOULD ALWAYS BE ACCOMPANIED BY ITS OBJECT. And this substantiates my point no. 2 that since, in your sentence, ‘have’ is used as a transitive verb, it should be followed by an object to complete the sentence or else it would be rendered incomplete (in the manner I have presented a corrected version, where ‘the one’ is the object of ‘has’ following
than)
Now note, that ‘to have’ can also be used as a helping verb
(classified as a non-transitive verb, since they are neither transitive nor intransitive) , as in sentence no. 5, where it is used as a helping verb. As such, in this sentence, the verb ‘has’ has no object and is correct the way it is written. Other examples of helping verbs are ‘to be’, ‘to do’, which can be used suitably to substitute main verbs as I has been demonstrated in the list (1 to 10) further.
Last, in any comparison sentence, the clause following than can employ the suitable helping verb instead of the main verb and thus eliminate redundancy in some cases associated with mentioning object after verb (in case of transitive) and thus make the sentence shorter and concise.
Re-writing sentences 1 to 10:
1. Kate walks faster than Jim does.
2. Humans live for a shorter span of time than turtles do.
3. Andy is taller than Bill (is).
4. Apples are more healthy to eat than caramels (are).
5. Today, Mr. Clarke has left for home earlier than he had (left) the day before.
6. Cezanne likes Andy more than she does Bill. (sounds awkward, but is correct, refer
MGMAT SC 5th edition for an identical sentence on pg. 130)
7. His sister slaps him harder than his brother does.
8. I have dreamt of going to Harvard more than I have of just starting up a new business venture. (Here, probably the main transitive verb could be eliminated, but object (clause following
than) is necessary to retain meaning)
9. I drive the car faster than my brother does.
10. I have a better bat than my brother does.
NOW FINALLY, going back to the original sentence,
C.
Veins have larger diameters, larger lumens, and thinner walls than do corresponding arteriesNote, ‘have’ is used transitively, as a result of which the sentence if modified to
‘Veins have larger diameters, larger lumens, and thinner walls than corresponding arteries have’would be incorrect. If you want to employ ‘have’ after than, rather correct it to
Veins have larger diameters, larger lumens, and thinner walls than those that corresponding arteries have.‘Those’ following than is the object of the second ‘have’ and is correct the way it is written here.
Hence, option C stands tall and straight as a grammatically correct-worded sentence.
PS: I know this was a long rambling of sorts…

but I hope this post helps in clarifying your doubt. Would love if an expert endorses this reasoning...